THE INTERPOLATION OF BREAKS IN TIDE CURVES FROM 

 RECORDING GAUGES 



To secure continuous record for a complete year at a time, for harmonic 



analysis. 



By W. Bell Dawson, M.A., D.Sc, M.Inst.C.E., F.R.S.C. 



One of the primary ends in view in the investigation of the tides, 

 is the prediction of the time and the height of high and low water for a 

 future year, published in the form of Tide Tables, by which these data 

 for the tide, day by day, may be known. To attain this end, three steps 

 are required: (1) A continuous series of observations in which the 

 height of the water is ascertained moment by moment with relation to 

 the time. Such observations are best obtained by a registering instru- 

 ment, which gives a record of the tide in the form of a continuous 

 curve. When reduced to a truly uniform datum level, and when all 

 time errors are eliminated, this curve gives the desired correlation of 

 height relatively to time. (2) An analysis of this tide curve, by which a 

 series of primary sinusoids are obtained as its components. These 

 sinusoids are represented by tidal constants which define their phase and 

 amplitude. (3) By re-combining these sinusoids, with their phases set 

 to correspond with the astronomical conditions of any future year, and 

 with amplitudes as found by observation at any given locality, the tide 

 curves for that year can be produced. These are called prediction curves ; 

 and from them the time and height of successive high and low waters 

 are read off, to constitute a Tide Table for the year. 



For such an analysis, it is essential to have an unbroken series of 

 tidal observations for a complete year at a time. A year is needed to 

 obtain the recurrence of astronomical conditions in the variously related 

 movements of the moon, as well as the solar elements. The year dealt 

 with may begin at any calendar date, however. 



If any break or interruption occurs from any cause, or if the obser- 

 vations are faulty or uncertain for a time, it is necesssary to complete 

 or replace the tide curves by some method of interpolation. If this 

 cannot be done, the period of observation up to the break must be set 

 aside and a fresh beginning made, in the endeavour to obtain a complete 

 year for analysis. Interruptions are more probable in winter, especially 



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